Solve for $x$ and $y$ using elimination. $\begin{align*}-x+y &= -2 \\ -8x+3y &= -6\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-3$ and the bottom equation by $1$ $\begin{align*}3x-3y &= 6\\ -8x+3y &= -6\end{align*}$ Add the top and bottom equations. $-5x = 0$ Divide both sides by $-5$ and reduce as necessary. $x = 0$ Substitute $0$ for $x$ in the top equation. $- 0+y = -2$ $y = -2$ $y = -2$ $y = -2$ The solution is $\enspace x = 0, \enspace y = -2$.